Monthly Archives: January 2021

Polyhedrons

My best friend, whose name was Garth, told me the best way to learn to play the game he called “Dee-an-dee” was to watch first. “My next-door neighbor will come over tomorrow,” he said. “Now I want to show you the dice.”

We sat at a folding table in his room. He plopped a ragged denim bag on the linoleum tabletop, loosened the drawstrings, and dumped out a pile of dice.

As they clattered to a stop, I saw familiar white bone dice with dark pips, which must have come from a Yahtzee game, and clear red casino dice with white pips. There were big ones and small ones. Among them were dice of different colors. Blue, green, brown—the colors weren’t bright but drab, and they didn’t have pips but numbers.

The unfamiliar is often invisible. Under my eyes, there was something new in the world, and it took a moment for my consciousness to adapt. Jumbled up in the melee of plastic and pips and numbers were odd-shaped solids. These weren’t normal cube dice. Instead of squares, their faces were triangles and pentagons.

Garth said, “They’re polyhedrons.”

I picked one up. Holding it between thumb and forefinger, I turned it around. It was blue with black numbers. The corners and edges were worn and discolored, like a dingy sock. Each face was a pentagon.

“How do you roll it?”

“Like normal dice.”

“How do you know what number it is?”

“It’s the number on top.”

Rolling it in my palm, I couldn’t see any top. I dropped it on the table. One side showed a “3” flat up.

Garth reached for a dice. “This one’s different. It only has four sides.” He showed me a pyramid. “You have to toss it up and twirl it, like this.”

The dice spun in the air. He turned it around where it landed. “The numbers at the bottom of the sides are all the same. I rolled a four.”

He tapped the top point with a finger. “I call them caltrops. Don’t step on these.”

Polyhedrons - Photo courtesy of Kevin Green
“Polyhedrons.”
A full set of role-playing game dice, plus an additional d20, marked from 0 to 9 twice, each series with its own color. Photo courtesy of Kevin Greene of California’s Bay Area. An “old-school” gamer, Kevin began playing D&D in the sixth grade with these dice and Holmes Basic, Eldritch Wizardry, and the Monster Manual in 1982.
platonic body noun
variants: platonic solid
: any of the five regular geometrical solids comprising the simple tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedron

polyhedron noun
pronounced ˌpä-lē-hē-drən
plural polyhedrons or polyhedra ˌpä-​lē-hē-​drə
: a solid formed by plane faces

—Webster’s

A modern set of role-playing game dice consists of six polyhedrons. Each dice is used to generate random numbers from 1 to the number of faces—or sides—it has. In game parlance, they are known by this upper limit: d4, d6, d8, d10, d12, and d20.

Five of them, the four-, six-, eight-, twelve-, and twenty-sided dice are platonic solids. Despite the name, Plato did not invent them, but the regular geometrical solids figure in his philosophy. In Timeaus, he associated each of them with a classical element: tetrahedron (d4), fire; cube (d6), earth; octahedron (d8), air; icosahedron (d20), water. The dodecahedron (d12) Plato associated with heavenly constellations.

The ten-sided dice (d10), the only one of the set not a platonic solid, was added in 1980. It is an irregular-faced decahedron called a pentagonal trapezohedron. It is used to generate decimal numbers, most commonly 1 to 10 and 1 to 100, the latter range by rolling two dice, one each for the tens and ones places.

When a d10 is not available, a d20 is rolled and the tens digit ignored. Early d20s were numbered from 0 to 9 twice, one series being marked with a dot or colored differently—as the numbers on Kevin’s d20 are colored red and blue. To make this dice perform its d20 function, it’s rolled with a d6. A 4 to 6 on the d6, adds ten to the roll.

Dwarven Lords vs. Wyrm

The earth shook. Limestone walls trembled. Yellow plumes of dust fell in straight lines from the great cavern’s ceiling onto rooftops and pavements of the dwarven city. While the ground rumbled, adults grabbed children and scurried under lintels, miners dove beneath timber shorings, crafters ducked under worktables.

Throrgardr’s inhabitants were accustomed to earthquakes. This one was stronger than usual, but the dwarves were confident that their buildings would stand it, and that the tremor would soon subside.

It did. But while crafters recovered their work and homemakers swept the dust, news came from the shaft below the city. The mining team there had broken into an enormous cavern. The miners were presumed dead, and something lurks in the open darkness of the Deepmost Caverns.

Astonished faces turned panic stricken when shouts came from the under-city quarters. A great serpentine beast emerged from the shaft. It breathed fire and lightning. Families fled the city as the colossal creature crept along the streets. Its scaly skin squeezed between homes and workshops. It scooped up stragglers in great claws. Ripping with gnashing teeth, it ate in a ravenous frenzy.

Now the heroes have assembled. Ten dwarven lords must enter the abandoned city to hunt down and destroy the wyrm.

Ten Dwarven Lords

The party consists of ten 12th-level dwarven lords, a representative from each clan.

Ability Scores

I rolled 3d6 mostly in order. That is, I rolled Strength then Constitution. If either result was below 9, I started again.

Five of the six abilities play into the encounter. Apart from the obvious, the bonus to saves vs. Spells (Wisdom) might be needed as the wyrm is a spell-user. I doubt the dwarves will have occasion to parlay with the creature, but I used Charisma to determine the chain of command within the party.

Adjustments

While I adjusted Intelligence and Wisdom down to raise Strength, I didn’t allow to lose any Wisdom bonus (see above). Though I guessed a dwarven lord wouldn’t care so much about knowing more languages, so I mined the ore out of Intelligence.

Dwarven Lords vs. Wyrm
For easy reference, I put the ten dwarven lords on a single sheet and the wyrm on an index card.

Equipment

Each dwarf is equipped with plate mail & shield and a sword, unless another magic weapon is at hand. All carry a backpack from which they may pull any standard equipment required.

Magic Items

Using the rules for NPC Magic Items (X53), each 12th-level dwarven lord has a 60% chance to have an item from each magic item subtable. Items not usable by dwarves are forfeit.

I rolled for each dwarf on the Wand/Staff/Rod table and was eventually rewarded with the only item they can use. I wasn’t sure what one would do with a rod of cancellation until I got a cursed armor result. The dwarf with AC 9 will discover his predicament when first struck.

Even the scroll results that are not spells are fairly useless to the dwarven party. I did get a treasure map showing the location of a magic item. I traded it immediately for a roll on the General Magic table (X44), which gave me a sword +1, +3 vs. dragons. Perhaps fate itself machinates against the wyrm.

On the subject of swords, I rolled the usual chance for intelligent swords and got two, one of which had a special purpose. Though, instead of dealing with another character, let alone two of them, I’m going to let the encounter with a primordial wyrm determine whether any swords gain intelligence.

I rerolled duplicates. I thought three potions of speed, however useful, were unimaginative. But I kept items that seemed to me to be useless in the scenario. Protection from undead scroll, dimunition potion, ring of animal control: should these items survive the wyrm’s breath, they may be useful to adventurers who discover the dwarven tombs.

Gender

Without rules to differentiate, B/X implies a setting in which equal numbers of male and female heroes set out on adventures and contend with ferocious monsters. Unless some reason dictates a character’s gender, I let a dice decide: odd male, even female. Of the ten, four are dwarven ladies.

Assault and Support Teams

I imagine the dwarves might conduct a raid on the wyrm’s position, if she’s stationary, or an ambush, if on the prowl. Either way, the party is divided into assault and support teams. The support team uses missile fire to weaken the enemy and keep it occupied, while the assault team closes for melee. I assigned dwarves to teams by weapon type—melee or missile.

Chain of Command

The dwarves are shown on the character sheet in command order, leader on the left. The assault team leader is the mission commander. If a team leader is out of combat for any reason, the next in command (to the right) takes charge to continue the mission.

Morale

Because the encounter is intended to simulate events, the dwarves’ morale is important. Like the wyrm, the dwarves might retreat, if combat goes badly, to regroup and return later. The morale of both teams is 10 as long as the mission commander is alive and fighting. Otherwise, it drops to 8. If the support team leader is out of combat, the team’s morale becomes 9 unless it joins the assault team.

Dwarven Lords' Character Sheet
The dwarven lords’ character sheet is color coded according to the table below. The ability scores match, more or less, to the sphere.

Color Sphere Ability
Red Melee Strength
Orange Missile Dexterity
Yellow Movement Charisma
Green Healing Constitution
Blue Protection Intelligence
Purple Utilities Wisdom

Names

Brisingi
f. flame

Rekkr
m. warrior, hero

Dagfinna
f. day finder

Thrasir
m. the one in rage

Aurvangr
m. mud field, gravely plain

Blainn
m. dark, blackish

Dorri
f. spearwoman

Herraud
f. army-peace

Ivaldi
m. yew bow wielder

Farli
m. the faring one

These few brave go to defend the dwarven home. Remember their names for the drinking halls will resound with songs to glorify their victory or dirges to mourn their deaths.

Primordial Wyrm

The primordial wyrm, a 16th-level monster, is 80’ long. Her serpentine body has eight legs and nascent wings. Though she cannot fly, she swims, and she climbs walls and ceilings as well as she crawls on the ground. She breathes fire and lightning. Being of dragon kind, she is vulnerable to attacks and magic vs. dragons.

The wyrm has a preternatural intelligence and the ability to speak, though not yet having been exposed, she knows no languages save that of magic.

After being awakened by the dwarves from a millenia-long slumber, she is hungry. For every dwarven lord (population) she eats, she can lay one egg.

The Wyrm Awakens

“They Delve too Deep. Draw a shaft off the bottom of the page.” (Dowler)

Dwarves who “delve too deep” is a fantasy staple—maybe a cliché. Whether it’s a balrog from the depths of the earth or an ambiguous nether-dwelling monster, in How to Host a Dungeon’s first edition (2008), the dwarves can hardly avert this end to their civilization. In the second edition, the too-deep delving can be avoided at a simple decision point, but the civilization’s end cannot.

I mentioned earlier that I want to use all the dwarven constructions, and there is still white space on the map. Through some rule-bending, I figured out how to do it. It will become clear later how that is achieved.

First, a fun diversion presents itself: The Throrgrmir dwarves have awakened the primordial wyrm. According to the rules, the civilization ends, and we move on to the Age of Monsters. But, in order to embellish the dungeon history for the subsequent campaign, I have the idea to simulate the battle between the dwarves and the wyrm with a B/X D&D encounter.1

Quick Math Using Mean Numbers

  • Ten 12th-level dwarves (a dwarven lord to represent each population token) versus a 16th-level dragon (the wyrm).2
  • Each dwarf has (4.5 x 9 + 9) 49 hit points and armor class 1 (platemail and shield with a +1 magic bonus).
  • The wyrm has (16 x 4.5) 72 hp and AC -3.3
  • In the first round of combat, the dwarves close for melee under the dragon’s breath weapon: Two dwarves (20%, they need a 4) fail the save vs. Dragon Breath and do not survive. Eight dwarves take half damage, 36 points, and are reduced to 13 hp.
  • In the second round, the dwarves attack. Assuming +2 “to hit” and damage for strength and magic weapons, dwarves need a 13 to deal damage. Of eight dwarves, five (65%) hit for (4.5 + 2) 6.5 points of damage each, which is 32 points, reducing the dragon to 40 hp.
  • The same round, the dragon wounds two more dwarves with its claws, and she bites another in half.
Rolling up dwarven lords
Rolling up dwarven lords for a B/X encounter.

So, the third combat round opens with a 40-hit-point wyrm versus seven dwarves, who could still take a claw to the face and do a collective 30 points of damage.

The scenario doesn’t account for the vagaries of combat, but the odds are close enough. I’m rolling up some dwarven lords. Let’s go wyrm hunting!

Notes

1 My first thought was to run the scenario using the Chainmail miniatures rules (Gygax and Perren, Guidon Games, 1971). As fun as that might be, the combat would be overly complex for the present purpose. Plus, this is a fantastic opportunity to exercise the D&D Expert Rulebook.

2 See the DONJON LANDS Level Tiers table below. Being primordial, the wyrm is mythic. The dwarven lords, from the Age of Civilization, are epic.

3 I considered the possibility that the wyrm could cast spells. In the quick scenario outlined here, however, the dragon’s best first-round action is a 72-point breath weapon [not to mention, in B/X, a dragon always attacks with its breath weapon first (B34)], and after the dwarves close for melee, she couldn’t get off a spell.

DONJON LANDS Level Tiers

Tier Character Levels Period Historical Age Dungeon Age*
Heroic 1-4 Medieval (Dark) Villainy
Legendary 5-8 Ancient Iron Monsters
Epic 9-12 Ancient Bronze Civilization
Mythic 13-16 Prehistoric Stone Primordial

*Ages from How to Host a Dungeon.

Throrgrmir’s Golden Age

Following the primordial earthquake that spawned the wyrm, seasons skipped across years, like stones on the river’s placid surface. Fairies frolicked in the primeval woods, while the river wound its way to the sea. Beneath it, water dripped from ceilings in subterranean caverns. Trickles crept between cold rock into dark flowing streams. Magma bubbled in deep chambers, and so, millennia passed while the wyrm slept, and the land, above and below, was quiet.

Then, wind rattled leaves in the old woods, and dwarves came rambling down from the western mountains. They sought gold, and they found it beneath the limestone hills and established a mine there. The vein was rich, the dwarves prospered, their number increased, and the Throrgrmir civilization, named for a founding father, was thus established.1

A note about the notes: As standard practice, I include the context in each footnote, so the reader may comfortably follow the narrative and read the notes afterward, using—if necessary—the superscript numbers for reference. The notes, while integral to the continuing story, are not essential to the immediate narrative.

As they mined the ore, the dwarves dug tunnels and built dormitories, treasure vaults, and workshops. Soon they caroused in a drinking hall,2 and a citadel3 enclosed the surface entrance to their underground domain.

Throrgrmir’s Golden Age
The Golden Age of Throrgrmir.
On the map, I mimic Dowler’s shapes from How to Host a Dungeon, and since I’m learning to draw, I mimic the style as well. In this photo, the tokens obscure the dungeon. See bottom for the civilization’s overlay extracted and a composite of the primordial and civilization ages.

The dwarves built a city in a great cavern, which they excavated from around the subterranean river.4 They erected a colossal statue of the founding father, which straddled the river where it entered the city.5 Throrgrmir flourished in a golden age of growth and prosperity.

From the crystal caverns, they mined gypsum, with which they covered the walls of their dwellings and carved into statues and course glasswork. They built a furnace and melted crystal,6 thus producing fine glassware tinted pink and blue. Over the river, they built a great bridge and, beyond it, a throne room, whence an emperor ruled over a mighty domain.

Led by pride and the search for new wealth, the dwarves dug a shaft below the city. Cutting through the last layer of granite, the miners broke into red limestone. The limestone, more porous and fragile, crumbled beneath them. The miners fell, with a great mass of rock, into the deepest caverns, where slept the wyrm.7

Notes

1 From lists of Norse dwarf names (see below), I derived Throrgrmir: thror (boar) + grmir (mask). I see adventurers finding ancient treasures stamped with a symbol of the masked boar, and three syllables with only two vowels sounds goodly dwarvish to my ear. When my human tongue stumbles over the name, dwarves only grunt their amusement.

Dwarf name sources:

2 Where the dwarves built inside the Dead Caverns (stratum 2), they used natural pathways between constructions. To guide travelers, they erected cairns along the paths (shown on the map). Counting five of these rock piles from the easternmost vault, one arrives at the drinking hall, known as “Sixth Cairn.”

3 I reserve the citadel’s face for a stylized symbol of the masked boar.

4 How to Host a Dungeon makes you think about things you might not otherwise consider. Example: While the dwarves used much of the excavated rock for building, future surface explorers will notice rubble strewn down hillsides and piled in ravines. Though it’s mostly limestone, also present are basalt and granite, the latter sometimes streaked with quartz. By then, the rubble may be covered by a layer of soil or overgrown by vegetation. Still, through close examination, clever delvers might infer, from the rubble, the existence of a nearby dungeon; from the amount, its size; and perhaps from the style of markings on discarded carvings, that dwarves built it. The presence of quartz, which often accompanies gold, might lead the greedy and the foolhardy to make bad decisions.

5 Note the detail inset of the colossal statue: In case of flood or invasion, the axe is lowered to dam the river and block the passage. Meanwhile, a chute opens in the hollow handle, which channels the flow through a tunnel to a point downstream, below the city.

6 Last week it was geology, this week I’m stretching chemistry thin over the fantasy. Some crystal, not selenite, can be melted into glass. In modern civilization, this decreases its value. But since glass is otherwise unknown in this age, Throrgrmir glassware is a valuable commodity in the milieu.

7 The dwarves’ blunder reformed the ceiling of the deepest cavern and deposited a huge pile of rubble into it, possibly creating an island in the lake. The event also rerouted the subterranean river, cutting it short and drying up the eastern loop.

milieu noun
pronounced mēl-yü
: the physical or social setting in which something occurs or develops : ENVIRONMENT

—Webster’s

[Popularized among old-school gamers by Gary Gygax, most notably in his Advanced D&D Dungeon Masters Guide (TSR Games, 1979), a 238-page work, wherein we find 72 instances.]

Throrgrmir’s Golden Age - overlay Throrgrmir’s Golden Age - composite
Throrgrmir Civilization Overlay and Composite.

Pebbles, Coins, Seashells, and Constructions

Symbols and Supplies

“These rules include a few symbols you should know… ⛭ Stands for epic treasure. These are optional….”
—Tony Dowler, How to Host a Dungeon

In the Supplies section of the rules, Dowler suggests using glass beads, coins, and board game tokens for the four symbols. I don’t have any beads, and I’m away from my games collection. I do have small change, though, and I’m spending the present lock-down near the sea.

Wyrm Dawn tokens for How to Host a Dungeon
I can’t imagine how epic treasure might be optional. I hope I’m playing this game right…

Flat, round, thumb-sized pebbles, fetched from the surf, do for populations. Shiny yellow ten-euro-cent pieces look like treasure. One-cent pieces, copper in color, are special bonuses, and seashells represent epic treasure.

Drawing

“There’s no right or wrong way to draw stuff, but there is a better and a worse way. The better way is one that’s pleasing to you and creates a dungeon you like.”

To draw the features in the age of civilization, Dowler suggests using a particular style to reflect the characteristics of the civilization that emerges following the primordial age. Dwarves, for example, build straight corridors at right angles. In construction, they use geometric shapes, often symmetrical. He also suggests using a different shape for each kind of construction.

Dwarven constructions for How to Host a Dungeon - Wyrm Dawn
To maintain a consistent size, I start with a circle—outline of a ten-cent coin—and draw the shape on and inside the edges. For larger constructions, like the power plant and throne room, I keep outside the circle. The city and battlefield are extra large, made with three circles.

According to my reading of the rules, the dwarves won’t have the opportunity to build all the rooms. But now that I’ve got shapes for them all, I might have to figure something out.

“The same goes for these rules…. You’ll probably get a better result following your instinct than worrying about the rules.”

Man, You’ve Got to Play This Game!

In the summer of 1982, I was 13 years old. The year before, I had moved with my family to another town half a state away from my first best friend. A few months later, he moved away too, and the kids in his new neighborhood played D&D.

I went to visit him in June. I remember that I had just arrived when he held up a thin, pale blue book and said, “Man, you’ve got to play this game!”

You only ever have one first best friend. Mine introduced me to DUNGEONS & DRAGONS.

Holmes Basic or Bluebook D&D
“Bluebook” D&D.
The 1977 edition of Gygax and Arneson’s DUNGEONS & DRAGONS is also known as “Holmes Basic” after editor Dr. J. Eric Holmes.

Primordial Wyrm

Using How to Host a Dungeon, the game map is divided into eight “strata” (enumerated on the right, map below). Each game stratum is made up of one or more geologic strata. I use the same term for both, I think without too much confusion. Each enumerated stratum also contains a feature. In Wyrm Dawn’s primordial age, many features are created by two rivers—one surface, another subsurface—and an earthquake.

Primordial Wyrm
Wyrm Dawn Campaign Map Cross-Section.
We are looking north. To the right is east; left west.

Here I describe each enumerated stratum. A table below summarizes.

1. Surface

A languid river meanders across its floodplain carved in a limestone bed. It deposits rich soil on its banks and seeps through porous rock to form a subterranean stream (stratum 4). From the soil grow lush grasses and primeval woods: deciduous on the flood plain, conifer higher up.

2. Dead Caves

Where the river spares the limestone, hills remain. Beneath them, limestone caverns, formed by river water in an earlier epoch, are now dry.1

3. Gold Vein

The result of an earthquake deep below the surface, the fissure struck through a layer of granite and quartz, forming the gold vein in an instant.2

4. Crystal Caverns

The subterranean stream comes out in this limestone layer to create these caverns. When the river runs nearer the hills, another stream gives into the western cave.3 A previous water line is still visible throughout the complex. Even where the stream doesn’t run, the caverns are still damp, creating selenite crystals.4, 5

5. Subterranean River

This subterranean river etches a course through limestone. It is swift but navigable from the east to where it falls through basalt (stratum 6).

6. Gem Deposits

A stratum of basalt contains gem deposits.

7. Magma Chamber

The earthquake also opened a fissure in this granite stratum from a magma source far below.

8. Mother of Dragons

Earth, shuddering in her labor, opened this large cavern complex to spawn a primordial wyrm. The parthenogenic creature emerged fully grown into the earth. She now seeks nourishment, so to lay her eggs.

Strata Summary

Stratum Primary rock Feature
1 Soil Biomes: deciduous and conifer woods, river, grassland, hills
2 Limestone, green6 Caves: connected caverns
3 Granite, quartz Ore: gold vein
4 Limestone, blue6 Biome: crystal caverns
5 Limestone, yellow6 Water: river
6 Basalt Gems: deposits
7 Granite Magma: chamber
8 Limestone, red6 Nexus: mother of monsters—dragons

 

The stage now set, the Age of Civilization begins.

Notes

1 A tunnel from the surface leads to the dead caves’ western cavern.
2 It seems our mundane world still wields much magic. A study described in this Nature article proposes that a gold vein can indeed be formed by an earthquake “in an instant.”
3 Like the dead caves above, a tunnel from the surface must lead down to the western cave mouth in the crystal caverns, while a tunnel to the eastern mouth is submerged. I’d look for a whirlpool in the surface river.
4 For the crystal caverns, I’m inspired by the selenite crystals from Mexico’s Naica cave.
5 Selenite, a variety of gypsum, is transparent and colorless, but impurities can give it a tinge of color, including blue and magenta, like a certain pair of game boxes—I’m going with that.
6 Who knew limestone comes in different colors? Savvy explorers might know how deep they have ventured by the kind and color of rock.

B/X D&D 40th-Anniversary Game

To celebrate the 40th anniversary of my favorite DUNGEONS & DRAGONS edition, I’m starting a new B/X campaign. Wyrmwyrd is a solo campaign, and I’m using Tony Dowler’s How to Host a Dungeon to create some back story. I think of it as a prequel campaign—working title: Wyrm Dawn. I just finished the primordial age. The mother of dragons spawned in the deepest caverns.

Wyrm Dawn
Wyrm Dawn Campaign Map with B/X D&D and Host to Host a Dungeon.

The original edition of D&D, created by Gary Gygax and Dave Arneson, was published in 1974. The edition known as “B/X” was edited by Tom Moldvay and David Cook with Steve Marsh and published as DUNGEONS & DRAGONS Fantasy Adventure Game Basic and Expert Rulebooks by TSR Hobbies, Lake Geneva, WI, in 1981 (first printing in January). How to Host a Dungeon: the solo game of dungeon creation by Tony Dowler is in its second edition (2019). The cross-section map is my own.