Works with Claude, ChatGPT, Gemini, or your own local model: paste this prompt and your AI will co-facilitate this exercise with you.

Help me prepare and run the exercise below. First ask for my participant count, time, setting, access needs and intended result. Check these against the stated limits. Use the supplied rules and materials. Explain any proposed changes before using them, and label them as adaptations. Do not invent source claims or require personal disclosure. Give me one step at a time when I say start. I manage the people, physical activity and clock; do not claim to observe the room. Ask me what happened before choosing a next step.

Reference revision: 3ff6e242bd287f914ec26b135e72960efe7d00580fa787e03b53e15a1240e4b7

# Equilateral Triangles Collaboration

Participants secretly select two peers and move silently through an open room until they form an equilateral triangle with them. The group reaches collective equilibrium through local adjustments without designated leadership.

**Time:** 15 minutes. WorkshopBank lists 30 minutes for 20+ people; UWT specifies 15 minutes for setup, a 1-to-3 minute movement run, a disruption test, and debrief.
**People:** 6 to 24. Whole group moving simultaneously in an open floor space.

## Choose this exercise

**Purpose:** Demonstrate how a group can reach collective equilibrium using a single local rule without central coordination.
**Use it when:** Use in an open room when launching a session on agile ways of working, self-organizing teams, or complex adaptive systems.
**Skip it when:** Skip if the group includes people who cannot navigate an open standing floor safely or if physical floor space is constrained.

## Materials and tools

- One stopwatch or phone timer for facilitator
- Scratch paper and pens for remote participants (if running remote variant)
- Shared digital whiteboard with numbered draggable tokens and three labeled sample tokens for demonstration (if running remote variant)

## Before participants arrive

1. Clear a large open space free of tables, chairs, and tripping hazards.
2. Ensure room perimeter has clear paths and chairs for anyone choosing an observer role.

## Say this to open

We are going to explore how groups organize under simple rules. Please stand and spread out across the open floor. Silently choose two other people in the room without signaling or pointing. Keep your choices private. Your goal is to position yourself so that you and your two chosen people form an equilateral triangle, meaning you are equal distance from both of them, and they are that same distance apart. When I say go, move without speaking until you reach your spot.

## How to run it

### 1. Demonstrate shape and choose targets (3 minutes)

State that there is no talking. Demonstrate an equilateral triangle using three volunteers positioned two paces apart to show three equal sides. Ask participants to spread out across the floor. Deliver the opening script. Direct everyone to silently choose two target people in the room without signaling or pointing.

### 2. Self-organize into position (4 minutes)

Say 'go' and start the stopwatch. Participants move around the room adjusting relative distances to their two targets. Target movement creates cascading adjustments across the room. Stop the timer when the group comes to a complete standstill, typically between 1 and 3 minutes. If motion continues past 3 minutes, pause the room.

### 3. Test system disruption (3 minutes)

Announce the elapsed time. Ask everyone to freeze and observe the resulting network. Ask one volunteer to take three large steps to the left and stop. Direct the room to silently re-adjust to restore their equilateral triangles with their chosen people. Note how quickly balance returns.

### 4. Debrief self-organization (5 minutes)

Gather the group in place or return to seats. Facilitate a debrief using the provided questions, taking three to four reflections from across the room.


## Debrief questions

- What happened to your position when the people you picked moved away?
- How long would this task take if one designated manager had to direct every person into position?
- What conditions allowed the group to reach balance without talking or a central coordinator?

**Finished output:** A stable spatial pattern reached through decentralized movement, followed by recorded observations on self-organizing systems.

## Remote

This physical movement game cannot be replicated directly in a video call. Run a labeled digital alternative on a shared virtual canvas. Pre-populate the canvas with three distinct sample tokens arranged in an equilateral triangle to show the geometry. Place numbered tokens across the board, assigning one token to each participant. Participants privately record two target numbers using scratch paper and pen without revealing them. When the facilitator says go, everyone drags their own token simultaneously to equalize distances between their token and their two target tokens. The facilitator calls stop once visible token dragging ceases across the board, then leads reflection on the resulting digital web.

## Hybrid

Hybrid delivery is not recommended because spatial movement cannot be shared equally between room and screen. Run fully remote using digital canvas tokens or fully in-person.

## Access and participation choices

- Participants with mobility limitations can act as the Timekeeper or the System Observer, tracking where shifts cascade across the room.
- Anyone may opt out of physical movement before the exercise starts, taking a seat at the edge without explanation.

## If the session gets stuck

**Movement never settles and people keep chasing each other in loops.**

After 3 minutes, call a brief pause. Remind participants that small adjustments work better than sprinting across the room, then restart the timer.

**Participants struggle to visualize the geometric goal during movement.**

Remind them of the opening demonstration: match the distance between yourself and your two partners to the distance separating those two partners.

**On a digital whiteboard, slight cursor jitters make it hard to confirm total stillness.**

Watch the broad token clusters rather than individual mouse twitches. Call stop when major relocations cease and tokens remain in their local spots for roughly 5 seconds.


## Terms used here

- Equilateral triangle: A three-sided geometric shape where all three sides are exactly the same length.

## Sources and adaptation

Observed in WorkshopBank as 'Equilateral Triangles Collaboration'. Also documented in systems thinking and complexity workshop traditions under names such as 'Triangles' or 'Systemic Constellations'.

Retained the core mechanic from WorkshopBank: participants choose two peers, form equilateral triangles without talking, and track elapsed time. WorkshopBank permits pointing, but UWT specifies silent and secret selection to prevent external coordination from short-circuiting self-organization. UWT adapted the group size from the source recommendation of 20+ people down to a range of 6 to 24, set a compact 15-minute schedule, added observer roles, incorporated a disruption test, and defined digital canvas rules and materials for remote teams.

[WorkshopBank](https://workshopbank.com/tools/equilateral-triangles-collaboration)

[WorkshopBank](https://workshopbank.com/equilateral-triangles-collaboration)

Current run sheet: https://unitedwetransform.com/exercises/equilateral-triangles-collaboration-workshopbank/